We study the problem of estimating conditional distribution functions from data containing additional errors. The only assumption on these errors is that a weighted sum of the absolute errors tends to zero with probability one for sample size tending to infinity. We prove sufficient conditions on the weights (e.g. fulfilled by kernel weights) of a local averaging estimate of the codf, based on data with errors, which ensure strong pointwise consistency. We show that two of the three sufficient conditions on the weights and a weaker version of the third one are also necessary for the spc. We also give sufficient conditions on the weights, which ensure a certain rate of convergence. As an application we estimate the codf of the number of cycles until failure based on data from experimental fatigue tests and use it as objective function in a shape optimization of a component.

我们研究从包含额外错误的数据中估计条件分布函数的问题。对这些误差的唯一假设是绝对误差的加权总和趋于零，样本大小趋于无穷大的概率为 1。我们证明了基于错误数据的本地平均估计值的权重（例如由内核权重满足）的充分条件，这确保了强大的逐点一致性。我们证明了权重的三个充分条件中的两个和第三个的较弱版本对于 spc 也是必要的。我们还给出了权重的充分条件，以确保一定的收敛速度。